Dong Yun Shin

Hyers-Ulam stability of functional equations in matrix normed spaces

In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces.MSC:47L25, 39B82, 46L07, 39B52.

Fuzzy Stability of Quadratic Functional Equations

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and    in fuzzy Banach spaces.

Fuzzy Stability of Jensen-Type Quadratic Functional Equations

We prove the generalized Hyers-Ulam stability of the following quadratic functional equations 2𝑓((𝑥

Generalized Ulam–Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation

Abstract Using the fixed point method, we prove the generalized Ulam–Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation.

STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN PROPER CQ -ALGEBRAS

In this paper, we prove the Hyers{Ulam{Rassias stability of the following additive functional inequality: ∥f(2x) + f(2y) + 2f(z)∥ � ∥ 2f(x + y + z)∥: (0.1) We investigate homomorphisms in proper CQ� -algebras and derivations on proper CQ � -algebras associated with the additive functional inequality (0.1).

Almost Jordan homomorphisms and Jordan derivations associated to the parametric-additive functional equation on fuzzy Banach algebras

AbstractIn this article, we establish the generalized Hyers-Ulam (or Hyers-Ulam-Rassais) stability of Jordan homomorphisms and Jordan derivations of the following parametric additive functional equation: ∑i=1mf(xi)=12m∑i=1mfmxi+∑j=1,j≠imxj+f∑i=1mxi for a fixed positive integer m with m ≥ 2, on fuzzy Banach algebras. The concept of Ulam-Hyers-Rassias stability originated from Rassias stability theorem that appeared in his article.Mathematics Subject Classification: Primary, 46S40; Secondary, 39B52; 39B82; 26E50; 46S50; 46H25.

On the Stability of Generalized Additive Functional Inequalities in Banach Spaces

We study the following generalized additive functional inequality , associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

Functional equations and inequalities in matrix paranormed spaces

In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality, the Cauchy additive functional equation and the quadratic functional equation in matrix paranormed spaces.MSC:47L25, 39B82, 39B72, 46L07, 39B52, 39B62.

C∗-ternary 3-derivations on InlineEquation

AbstractIn this paper, we prove the Hyers-Ulam stability of C∗-ternary 3-derivations and of C∗-ternary 3-homomorphisms for the functional equation f(x1+x2,y1+y2,z1+z2)=∑1≤i,j,k≤2f(xi,yj,zk) in C∗-ternary algebras.MSC:17A40, 39B52, 46Lxx, 46K70, 46L05, 46B99.In this paper, we prove the Hyers-Ulam stability of C ∗ Open image in new window-ternary 3-derivations and of C ∗ Open image in new window-ternary 3-homomorphisms for the functional equation

Functional equations in paranormed spaces

In this paper, we prove the Hyers-Ulam stability of various functional equations in paranormed spaces.MSC:35A17, 39B52, 39B72.